Two-dimensional Time-dependent Point Interactions

zbMath1372.81038arXiv1601.02390MaRDI QIDQ5355532

Raffaele Carlone, Rodolfo Figari, Michele Correggi

Publication date: 7 September 2017

Full work available at URL: https://arxiv.org/abs/1601.02390

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Many-body theory; quantum Hall effect (81V70) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Time-dependent Schrödinger equations and Dirac equations (35Q41) Special quantum systems, such as solvable systems (81Q80)

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The point-like limit for a NLS equation with concentrated nonlinearity in dimension three ⋮ Ground states for the planar NLSE with a point defect as minimizers of the constrained energy ⋮ Complete ionization for a non-autonomous point interaction model in \(\mathrm{d}=2\) ⋮ Numerical approximation of the Schrödinger equation with concentrated potential ⋮ Blow-up for the pointwise NLS in dimension two: absence of critical power ⋮ Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity ⋮ Emergence of Time-Dependent Point Interactions in Polaron Models ⋮ Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one ⋮ The action of Volterra integral operators with highly singular kernels on Hölder continuous, Lebesgue and Sobolev functions

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